Graphs of Functions and Their Derivatives

Given the table of R(t), estimate R'(10).

• 33

• 42

• 9

• 9/4

• 9/10

Water flows into a tank for 24 hours. R(t) represents the gallons of water in the tank at t hours. What does R'(t) represent? Check all that apply.

• the amount of water in the tank in gallons

• the rate of change of the water at t hours

• the speed of the water flow at t hours

• gallons per hour

Describe how to estimate f'(1) given the table of values for f(x) = 0.5x^3 - 2.

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Is the above function differentiable for all values of x? Why?

• Yes, the slope of the tangent line can be calculated for all values of x.

• Yes, the function is continuous for all values of x so the function is differentiable.

• No, the function has a sharp turn in the first quadrant so if is not differentiable.

• No, the function is discontinuous so it is not differentiable.

In which quadrant of the graph above will there be a value of x that is non-differentiable?

• 1

• 2

• 3

• 4

Is the above function differentiable at

x = 0? Why?

• Yes. The derivative would be equal to zero since there is a vertical tangent.

• No. The derivative would not exist at x = 0 since there is a vertical tangent.

Check off all of the words that also mean derivative.

• instantaneous rate of change

• average rate of change

• slope at a point

• slope of a secant line

• slope of a tangent line

Let y = 2x³ - 4x + 6. Find y'' (derivative of the derivative)

• 6x² - 4

• 12x - 4

• 12x

• 6x